Coord3D: 3D coordinate vector R6 Class
In affiner: A Finer Way to Render 3D Illustrated Objects in 'grid' Using Affine Transformations
Coord3D R Documentation
3D coordinate vector R6 Class
Description
Coord3D is an R6::R6Class() object representing three-dimensional points
represented by Cartesian Coordinates.
Active bindings
xyzwA four-column matrix representing the homogeneous coordinates.
The first three columns are "x", "y", and "z" coordinates
and the fourth column is all ones.
xA numeric vector of x-coordinates.
yA numeric vector of y-coordinates.
zA numeric vector of z-coordinates.
Methods
Public methods
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Method new()
Usage
Coord3D$new(xyzw)
Arguments
xyzwA matrix with four columns representing (homogeneous) coordinates.
The first three columns represent x, y, and z coordinates and
the last column is all ones.
Column names should be "x", "y", "z", and "w".
Method permute()
Usage
Coord3D$permute(permutation = c("xyz", "xzy", "yxz", "yzx", "zyx", "zxy"))
Arguments
permutationEither "xyz" (no permutation), "xzy" (permute y and z axes),
"yxz" (permute x and y axes), "yzx" (x becomes z, y becomes x, z becomes y),
"zxy" (x becomes y, y becomes z, z becomes x), "zyx" (permute x and z axes)
Method print()
Usage
Coord3D$print(n = NULL, ...)
Arguments
nNumber of coordinates to print. If NULL print all of them.
...Passed to format.default().
Method project()
Usage
Coord3D$project(
plane = as_plane3d("xy-plane"),
...,
scale = 0,
alpha = angle(45, "degrees")
)
Arguments
planeA Plane3D object of length one representing the plane
you wish to reflect across or project to or an object coercible to one using as_plane3d(plane, ...)
such as "xy-plane", "xz-plane", or "yz-plane".
...Passed to project3d().
scaleOblique projection foreshortening scale factor.
A (degenerate) 0 value indicates an orthographic projection.
A value of 0.5 is used by a “cabinet projection”
while a value of 1.0 is used by a “cavalier projection”.
alphaOblique projection angle (the angle the third axis is projected going off at).
An angle() object or one coercible to one with as_angle(alpha, ...).
Popular angles are 45 degrees, 60 degrees, and arctangent(2) degrees.
Method reflect()
Usage
Coord3D$reflect(plane = as_plane3d("xy-plane"), ...)
Arguments
planeA Plane3D object of length one representing the plane
you wish to reflect across or project to or an object coercible to one using as_plane3d(plane, ...)
such as "xy-plane", "xz-plane", or "yz-plane".
...Passed to reflect3d().
Method rotate()
Usage
Coord3D$rotate(axis = as_coord3d("z-axis"), theta = angle(0), ...)
Arguments
axisA Coord3D class object or one that can coerced to one by as_coord3d(axis, ...).
The axis represents the axis to be rotated around.
thetaAn angle() object of length one or an object coercible to one by as_angle(theta, ...).
...Passed to rotate3d().
Method scale()
Usage
Coord3D$scale(x_scale = 1, y_scale = x_scale, z_scale = x_scale)
Arguments
x_scaleScaling factor to apply to x coordinates
y_scaleScaling factor to apply to y coordinates
z_scaleScaling factor to apply to z coordinates
Method shear()
Usage
Coord3D$shear(
xy_shear = 0,
xz_shear = 0,
yx_shear = 0,
yz_shear = 0,
zx_shear = 0,
zy_shear = 0
)
Arguments
xy_shearShear factor: x = x + xy_shear * y + xz_shear * z
xz_shearShear factor: x = x + xy_shear * y + xz_shear * z
yx_shearShear factor: y = yx_shear * x + y + yz_shear * z
yz_shearShear factor: y = yx_shear * x + y + yz_shear * z
zx_shearShear factor: z = zx_shear * x + zy_shear * y + z
zy_shearShear factor: z = zx_shear * x + zy_shear * y + z
Method translate()
Usage
Coord3D$translate(x = as_coord3d(0, 0, 0), ...)
Arguments
xA Coord3D object of length one or an object coercible to one by as_coord3d(x, ...).
...Passed to as_coord3d(x, ...) if x is not a Coord3D object
Method transform()
Usage
Coord3D$transform(mat = transform3d())
Arguments
matA 4x4 matrix representing a post-multiplied affine transformation matrix.
The last column must be equal to c(0, 0, 0, 1).
If the last row is c(0, 0, 0, 1) you may need to transpose it
to convert it from a pre-multiplied affine transformation matrix to a post-multiplied one.
If a 3x3 matrix (such as a 3x3 post-multiplied 3D rotation matrix)
we'll quietly add a final column/row equal to c(0, 0, 0, 1).
Method clone()
The objects of this class are cloneable with this method.
Usage
Coord3D$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
Examples
p <- as_coord3d(x = rnorm(100, 2), y = rnorm(100, 2), z = rnorm(100, 2))
print(p, n = 10)
pc <- mean(p) # Centroid
# method chained affine transformation matrices are auto-pre-multiplied
p$
translate(-pc)$
reflect("xy-plane")$
rotate("z-axis", degrees(90))$
print(n = 10)
affiner documentation built on April 4, 2025, 4:42 a.m.
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| Coord3D | R Documentation |
3D coordinate vector R6 Class
Description
Coord3D is an R6::R6Class() object representing three-dimensional points
represented by Cartesian Coordinates.
Active bindings
xyzwA four-column matrix representing the homogeneous coordinates. The first three columns are "x", "y", and "z" coordinates and the fourth column is all ones.
xA numeric vector of x-coordinates.
yA numeric vector of y-coordinates.
zA numeric vector of z-coordinates.
Methods
Public methods
Method new()
Usage
Coord3D$new(xyzw)
Arguments
xyzwA matrix with four columns representing (homogeneous) coordinates. The first three columns represent x, y, and z coordinates and the last column is all ones. Column names should be "x", "y", "z", and "w".
Method permute()
Usage
Coord3D$permute(permutation = c("xyz", "xzy", "yxz", "yzx", "zyx", "zxy"))Arguments
permutationEither "xyz" (no permutation), "xzy" (permute y and z axes), "yxz" (permute x and y axes), "yzx" (x becomes z, y becomes x, z becomes y), "zxy" (x becomes y, y becomes z, z becomes x), "zyx" (permute x and z axes)
Method print()
Usage
Coord3D$print(n = NULL, ...)
Arguments
nNumber of coordinates to print. If
NULLprint all of them....Passed to
format.default().
Method project()
Usage
Coord3D$project(
plane = as_plane3d("xy-plane"),
...,
scale = 0,
alpha = angle(45, "degrees")
)Arguments
planeA Plane3D object of length one representing the plane you wish to reflect across or project to or an object coercible to one using
as_plane3d(plane, ...)such as "xy-plane", "xz-plane", or "yz-plane"....Passed to
project3d().scaleOblique projection foreshortening scale factor. A (degenerate)
0value indicates an orthographic projection. A value of0.5is used by a “cabinet projection” while a value of1.0is used by a “cavalier projection”.alphaOblique projection angle (the angle the third axis is projected going off at). An
angle()object or one coercible to one withas_angle(alpha, ...). Popular angles are 45 degrees, 60 degrees, andarctangent(2)degrees.
Method reflect()
Usage
Coord3D$reflect(plane = as_plane3d("xy-plane"), ...)Arguments
planeA Plane3D object of length one representing the plane you wish to reflect across or project to or an object coercible to one using
as_plane3d(plane, ...)such as "xy-plane", "xz-plane", or "yz-plane"....Passed to
reflect3d().
Method rotate()
Usage
Coord3D$rotate(axis = as_coord3d("z-axis"), theta = angle(0), ...)Arguments
axisA Coord3D class object or one that can coerced to one by
as_coord3d(axis, ...). Theaxisrepresents the axis to be rotated around.thetaAn
angle()object of length one or an object coercible to one byas_angle(theta, ...)....Passed to
rotate3d().
Method scale()
Usage
Coord3D$scale(x_scale = 1, y_scale = x_scale, z_scale = x_scale)
Arguments
x_scaleScaling factor to apply to x coordinates
y_scaleScaling factor to apply to y coordinates
z_scaleScaling factor to apply to z coordinates
Method shear()
Usage
Coord3D$shear( xy_shear = 0, xz_shear = 0, yx_shear = 0, yz_shear = 0, zx_shear = 0, zy_shear = 0 )
Arguments
xy_shearShear factor:
x = x + xy_shear * y + xz_shear * zxz_shearShear factor:
x = x + xy_shear * y + xz_shear * zyx_shearShear factor:
y = yx_shear * x + y + yz_shear * zyz_shearShear factor:
y = yx_shear * x + y + yz_shear * zzx_shearShear factor:
z = zx_shear * x + zy_shear * y + zzy_shearShear factor:
z = zx_shear * x + zy_shear * y + z
Method translate()
Usage
Coord3D$translate(x = as_coord3d(0, 0, 0), ...)
Arguments
xA Coord3D object of length one or an object coercible to one by
as_coord3d(x, ...)....Passed to
as_coord3d(x, ...)ifxis not a Coord3D object
Method transform()
Usage
Coord3D$transform(mat = transform3d())
Arguments
matA 4x4 matrix representing a post-multiplied affine transformation matrix. The last column must be equal to
c(0, 0, 0, 1). If the last row isc(0, 0, 0, 1)you may need to transpose it to convert it from a pre-multiplied affine transformation matrix to a post-multiplied one. If a 3x3 matrix (such as a 3x3 post-multiplied 3D rotation matrix) we'll quietly add a final column/row equal toc(0, 0, 0, 1).
Method clone()
The objects of this class are cloneable with this method.
Usage
Coord3D$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
Examples
p <- as_coord3d(x = rnorm(100, 2), y = rnorm(100, 2), z = rnorm(100, 2))
print(p, n = 10)
pc <- mean(p) # Centroid
# method chained affine transformation matrices are auto-pre-multiplied
p$
translate(-pc)$
reflect("xy-plane")$
rotate("z-axis", degrees(90))$
print(n = 10)
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